Question
Which of the following points is a solution of the inequality \( y<|x-2| \) ? \( (2,0) \) \( (2,1) \) \( (-2,0) \)
Ask by Blake Beck. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The point (-2,0) satisfies the inequality \( y < |x - 2| \).
Solution
To determine which point satisfies the inequality y < |x - 2|, substitute each point into the inequality.
For (2,0):
y = 0 and x = 2.
Inequality: 0 < |2 - 2| = |0| = 0.
Since 0 is not less than 0, (2,0) does not satisfy the inequality.
For (2,1):
y = 1 and x = 2.
Inequality: 1 < |2 - 2| = |0| = 0.
Since 1 is not less than 0, (2,1) does not satisfy the inequality.
For (-2,0):
y = 0 and x = -2.
Inequality: 0 < |(-2) - 2| = |-4| = 4.
Since 0 is less than 4, (-2,0) satisfies the inequality.
Thus, the point (-2,0) is a solution of the inequality y < |x-2|.
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Simplify this solution The Deep Dive
To determine which points are solutions to the inequality \( y < |x-2| \), we can substitute each point into the inequality. For the point \( (2,0) \): \[ 0 < |2-2| \] \[ 0 < 0 \] (False) For the point \( (2,1) \): \[ 1 < |2-2| \] \[ 1 < 0 \] (False) For the point \( (-2,0) \): \[ 0 < |-2-2| \] \[ 0 < 4 \] (True) So, the point \( (-2,0) \) is a solution to the inequality \( y < |x-2| \).
